Hahaha — who knew that “Quaithe is Daenerys from the future” would be the most controversial thing I ever said?
Okay, let me begin by stating for the record that I’m not throwing down some kind of gauntlet here. I’m not 100% POSITIVELY MAKING THE DEFINITIVE CASE THAT QUAITHE IS FUTURE DAENERYS, THE EVIDENCE IS ALL THERE IF YOU HAVE THE EYES TO SEE IT, AND IN FACT BASED ON THIS INCONTROVERTIBLE FACT WE CAN ALSO CLEARLY STATE THAT AEGON IS REAL AND PATCHFACE IS THE GREAT OTHER AND OLD NAN WAS IN THE PASTE THAT BRAN ATE AND HEY WHY ARE YOU LOOKING AT ME LIKE THAT. That’s just not how I roll with theories and predictions. “Quaithe is Dany from the future” is just a fun answer to an idle question, is all.
Do I think it might have some basis in the text? Yeah, some: weirwoods see all time existing cotemporaneously, and human beings gifted with greensight can access them and see time in the same fashion, and even make themselves heard through the trees’ leaves to an extent. That’s a tiny step along the path to full-fledged “appearing to your past self in the flesh from time to time,” but a step is a step.
Beyond that? It’d help explain why Quaithe wears the mask — I know there’s a cultural explanation, but what better way to hide your identity than to take up the guide of a culture that does so as a default. It’d help explain why she’s so cryptic, in the way that “notes from your future self” SFF stories frequently do — you need to guide yourself along the path and get yourself to do everything you need yourself to do but still make them earn it because you require the hard-earned wisdom they gain along the way, which would be lost if you just popped up and said “do this and do that.” (See also the nature of prophecy itself.)
I would also note that I don’t think there’s anything more or less fantasy OR science-fiction about time travel of this sort than about dragons or zombies or clairvoyance or resurrection or any of the other magic we’ve seen at play, all of which can and have been depicted in genre fiction as having pseudoscientific explanations in the past.
Finally, it’s just a fun thing to say. Try it! “Quaithe is Daenerys from the future. It is known.” See???